Estimation of Surface Roughness Parameters Using Fractal and Close Range Photogrammetric Methods

Nowadays, surface roughness measurement has been considered in many civil and industrial applications. One of the important indicators in measuring the roughness of the surface, is determining the fractal dimension. To determine the fractal dimension, the profile meters are usually used by contact method, which in the case of surfaces with low roughness may cause distortion of the surface texture and as a result, the roughness is measured with low accuracy. In this study, a fast and reliable method based on close range photogrammetry, which is a non-contact method, for measuring fractal dimension and roughness is presented. The case study in this research is the sand surface.. Digital elevation model was created by taking several overlapped photographs. For accurate measurements on the surface 6 control points were created, then scaling and definition of the coordinate system was performed. The accuracy in x-y plane is 1.33 mm and the height accuracy is 0.32 mm. In order to measure the surface roughness parameters including correlation length and root mean square height (rms-height), several profiles were extracted from the three-dimensional surface. The slope of the surface spectrum was calculated using Welch method for each of these profiles then the fractal dimensions were calculated. Finally, using the fractal dimension, the correlation length and rms-height were calculated for each of the profiles. In this study, surface roughness was evaluated using four indices of fractal dimension, correlation length, rms-height and ZS parameter (ratio of rms-height to correlation length). ‌ The results showed that for all profiles, ZS with 81% correlation coefficient with fractal dimension, is a sufficient indicator for calculating the surface roughness, because of the the independence of this indicator from the length of the profile. This study showed that the close-range photogrammetry is a very suitable and reliable method for measuring roughness parameters. One of the important advantages of this method, unlike other methods such as needle or laser profile meters, is having multiple profiles in any desired direction and preserve of texture (especially on very low roughness surfaces) due to direct contact of the profile meter with the surface.